id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
40,711 |
x_{i + 1} = x_{1 + i}
|
32,919 |
\dfrac1x + 1/M + 1/N = (x*M + M*N + N*x)/(x*N*M)
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-18,437 |
\frac{r}{\left(r + 7 \cdot (-1)\right) \cdot (r + 2)} \cdot \left(7 \cdot (-1) + r\right) = \frac{1}{14 \cdot (-1) + r^2 - 5 \cdot r} \cdot \left(r^2 - 7 \cdot r\right)
|
11,962 |
0 = \overline{\sum_{k=0}^n a_k\cdot z^k} = \sum_{k=0}^n a_k\cdot \overline{z}^k
|
15,214 |
s = s/2 + \tfrac{s}{2} < \frac{s}{2} + 1
|
-4,114 |
\dfrac{1}{a^3} \cdot a \cdot a = \tfrac{a \cdot a}{a \cdot a \cdot a} = 1/a
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-1,497 |
-2/9 \cdot \left(-5/7\right) = \frac{\dfrac19 \cdot \left(-2\right)}{1/5 \cdot (-7)}
|
1,663 |
v_1 \lambda = Bv_1 \Rightarrow B^2 v_1 = \lambda Bv_1 = \lambda * \lambda v_1
|
-1,247 |
\tfrac{30}{35} = \dfrac{1}{35*\frac{1}{5}}*6 = 6/7
|
9,523 |
\frac{10}{20}\cdot \tfrac14 = 1/8
|
22,346 |
-D \cdot 2 + D^2 = 0 \Rightarrow 0 = D,2
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24,367 |
\int g\,\text{d}z = \lim_{m \to \infty} \int g_m\,\text{d}z = \int \lim_{m \to \infty} g_m\,\text{d}z
|
-18,986 |
\dfrac15 = \dfrac{1}{49 \cdot \pi} \cdot G_t \cdot 49 \cdot \pi = G_t
|
35,639 |
1/8 = \frac{3 * 3^2}{6 * 6^2}
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17,716 |
12 = 2\cdot 6 + 0(-1)
|
7,925 |
5 + y^2 - 4y = 1 + (y + 2\left(-1\right))^2
|
3,637 |
((x + 1)^2 - x^2)/x = (x^2 + 2*x + 1 - x^2)/x = \frac1x*(2*x + 1)
|
36,075 |
\frac{1}{-27} = -\frac{1}{27}
|
-4,357 |
\dfrac{10}{7} \cdot q^2 = q^2 \cdot 10/7
|
-8,314 |
8 (-7) = -56
|
28,431 |
0 = \lim_{l \to \infty} |a_l|\Longrightarrow \lim_{l \to \infty} a_l = 0
|
14,935 |
u \cdot u\cdot 2 + v \cdot v = v + 4\cdot u \Rightarrow 2\cdot u^2 - u\cdot 4 + v^2 - v = 0
|
-7,847 |
\dfrac{28 + i*6}{4 - 2i} = \frac{i*6 + 28}{-i*2 + 4} \frac{1}{4 + 2i}(4 + i*2)
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-23,265 |
1 - \frac13 = \frac{2}{3}
|
25,128 |
\gamma_x \cdot \gamma_x - 2\cdot t\cdot \gamma_x + x = 0 = (\gamma_x - t)^2
|
7,384 |
-q\cdot k = -k\cdot q
|
6,400 |
x \times (C + Y) = Y \times x + x \times C
|
21,286 |
Y\cdot A\cdot x_2 = A\cdot Y\cdot x_2
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32,771 |
2×(2×2×2×2)=32
|
-16,515 |
\sqrt{25\cdot 11}\cdot 6 = \sqrt{275}\cdot 6
|
17,504 |
b^2 + ba = b^2 + ab
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-11,973 |
1/3 = \frac{p}{10\cdot \pi}\cdot 10\cdot \pi = p
|
22,177 |
1 = 1/2 + \frac14 + \dfrac{1}{6} + \dfrac{1}{12}
|
33,691 |
\frac22 \cdot 1 = \frac{6}{2 \cdot 3}
|
2,559 |
6 \cdot (0.1 + 0.5) + (0.3 + 0.1) \cdot 3 = 4.8
|
23,557 |
\left(h - b\right)*(h^2 + b*h + b^2) = -b^3 + h^2 * h
|
-11,468 |
0 + 6*(-1) + i*8 = -6 + i*8
|
18,031 |
2^l = 2^{(-1) + l} + 2^{(-1) + l}
|
2,497 |
d + 1 = \left(d + 1\right)^2 = d \cdot d + 2 \cdot d + 1
|
43 |
(D\times x\times D^X)^X = (D^X)^X\times x^X\times D^X = D\times x\times D^X
|
3,572 |
z_2 = 0, z_1 \neq 0 \Rightarrow 0 = \tfrac{z_1}{z_1^2 + z_2^4} z_2^2
|
8,829 |
2 \cdot (4 \cdot x^2 - 3 \cdot x + (-1)) = 2 \cdot (x + (-1)) \cdot (x + \frac{1}{4}) = \frac{1}{2 \cdot \left(x + (-1)\right) \cdot (4 \cdot x + 1)}
|
3,442 |
7/8 + 8/8 + 6.5 \cdot \frac{3}{4} = 6.75
|
3,343 |
n^2 - -n + n^2 = n
|
-2,681 |
\sqrt{7}\cdot 11 = \sqrt{7}\cdot (5 + 4 + 2)
|
-7,660 |
\frac{1 - i \cdot 7}{-3 - 4 \cdot i} = \dfrac{-i \cdot 7 + 1}{-3 - 4 \cdot i} \cdot \dfrac{-3 + 4 \cdot i}{-3 + 4 \cdot i}
|
16,007 |
-6\cdot (a + b + c) = (a + b + c)^2\cdot 2 - 3\cdot b\cdot a - 3\cdot b\cdot c - c\cdot a\cdot 3 rightarrow 0 = a\cdot b + b\cdot c + a\cdot c
|
-13,640 |
\frac{30}{5 + 1} = \frac{30}{6} = 30/6 = 5
|
33,691 |
\dfrac13\cdot 6/2 = 6/(3\cdot 2)
|
12,880 |
m\cdot 6 + 1 + 1 = 2 + m\cdot 6
|
16,071 |
1/4 + 1/4\cdot 2 = 3/4 \lt 1
|
6,730 |
x^{b_1 + b_2} = x^{b_1}\cdot x^{b_2}
|
37,568 |
\frac{q^2 - q}{n \cdot n - n} + \frac{1}{n^2 - n}\cdot \left(q\cdot n - q^2\right) = \frac{1}{n^2 - n}\cdot (q^2 + q\cdot n - q^2 - q) = \frac{q\cdot n - q}{n \cdot n - n}
|
28,107 |
64 + 40\cdot (-1) = 24
|
-6,301 |
\frac{1}{2 \cdot \left(5 \cdot (-1) + h\right)} \cdot 5 = \dfrac{1}{10 \cdot (-1) + 2 \cdot h} \cdot 5
|
16,989 |
(x*3)^2 = 9x^2
|
-4,748 |
x \cdot x - 7\cdot x + 12 = (x + 3\cdot \left(-1\right))\cdot (4\cdot (-1) + x)
|
-30,853 |
\frac{z^3 - 9 \times z}{-3 \times z + z^2} = z + 3
|
13,406 |
3 < l \leq 4\Longrightarrow l = 4
|
-9,351 |
-z^2\cdot 121 = -11\cdot 11 z z
|
26,163 |
15 \cdot 200 = 3000
|
-744 |
(e^{\pi \cdot i \cdot 7/12})^{13} = e^{13 \cdot 7 \cdot \pi \cdot i/12}
|
11,415 |
0 + u + v + 0 = 0 + v + u + 0\Longrightarrow u + v = u + v
|
6,332 |
n = n + (-1) + 1 = n + 2*\left(-1\right) + 2 = \dots = \frac12*\left(n + 1\right) + \frac{1}{2}*(n + (-1))
|
7,009 |
-1 = (-1)^{1/2}*(-1)^{1/2} = (\left(-1\right)*(-1))^{1/2} = 1^{1/2} = 1
|
28,473 |
441 + 4(-1) = 19*23
|
25,412 |
a*b = b*a/a*a
|
21,722 |
1/10 + 1/15 = \dfrac{3}{30} + 2/30 = 5/30
|
33,608 |
\dfrac{1}{12}\cdot ((-1) + 6 \cdot 6) = \frac{1}{12}\cdot 35
|
48,352 |
0 = b \frac{-c^3}{b^2} + c \frac{-c}{b} = \frac{ -c^3-c^2b } { b^2} = - \frac{ c^2 (c+b) } {b^2}
|
15,562 |
\frac{\dfrac1y \cdot y}{y \cdot x} = \dfrac{1}{y \cdot x}
|
-2,575 |
\sqrt{5}\cdot (3 + 2\cdot (-1)) = \sqrt{5}
|
4,045 |
\frac1n \cdot k = \frac{k}{n}
|
-16,427 |
2(16*11)^{\frac{1}{2}} = 176^{\frac{1}{2}}*2
|
-2,886 |
\sqrt{2}*7 = \sqrt{2}*(5 + 4 + 2*(-1))
|
-20,506 |
\dfrac{n \cdot (-10)}{(-1) \cdot 10 \cdot n} \cdot (-\tfrac{1}{5}) = \dfrac{n \cdot 10}{(-1) \cdot 50 \cdot n}
|
-5,127 |
10^5 \cdot 0.79 = 0.79 \cdot 10^{2 - -3}
|
-21,039 |
\frac18\cdot (g + 5\cdot (-1))\cdot 7/7 = \frac{1}{56}\cdot (35\cdot \left(-1\right) + 7\cdot g)
|
-11,590 |
0 + 12\times (-1) - i\times 9 = -12 - i\times 9
|
32,955 |
495 = \tfrac{12!}{8!\cdot 4!}
|
-25,245 |
-\dfrac{4}{2^5} = -\dfrac{4}{32} = -1/8
|
8,215 |
0 = -2*z_1 * z_1 + 8*z_2 \implies 4*z_2 = z_1^2
|
-26,924 |
\sum_{m=1}^\infty \frac{3\times \left(3 + 1\right)^m}{m\times 4^m} = \sum_{m=1}^\infty \frac{3\times 4^m}{m\times 4^m} = \sum_{m=1}^\infty \frac{3}{m} = 3\times \sum_{m=1}^\infty 1/m
|
11,571 |
x^4 + 10 x^2 + 25 = (x^2 + 5)^2 = \left(2*3^{1 / 2} x\right)^2 = 12 x^2
|
9,543 |
\left(8 \cdot 8 + 16^2\right)^{1/2} = 8\cdot 5^{1/2}
|
10,598 |
10^2 = \frac{2}{2} \cdot 10^2 = \frac33 \cdot 10^2 = \cdots
|
-20,133 |
-1/10 \cdot \frac{(-8) \cdot z}{(-8) \cdot z} = \frac{8 \cdot z}{z \cdot \left(-80\right)}
|
27,088 |
\left(-4\right)^2 + 3 * 3 = (-4 + 1)^2 + (1 + 3)^2
|
16,799 |
\tan^{-1}(\infty) = \dfrac{1}{2}*\pi
|
7,649 |
b/x = \frac1x\cdot b
|
-1,653 |
\frac{1}{3} 5 \pi + \pi*3/4 = \pi*29/12
|
-5,940 |
\dfrac{5}{2\cdot h + 4} = \frac{1}{(2 + h)\cdot 2}\cdot 5
|
16,813 |
-x_3 + x_2 = 4 \Rightarrow 8 = 2 \cdot x_2 - 2 \cdot x_3
|
2,337 |
\frac{1}{1/T*M*T} = \frac{1}{T}*\frac{1}{M}*T
|
13,499 |
\left(1 + p^2\right) (1 + p^4 - p^2) = 1 + p^6
|
-20,809 |
\frac{-6 \cdot k + 10 \cdot (-1)}{-k \cdot 6 + 10 \cdot (-1)} \cdot (-\frac19 \cdot 4) = \frac{1}{90 \cdot \left(-1\right) - 54 \cdot k} \cdot (40 + k \cdot 24)
|
-26,213 |
(6 - 14\cdot y)\cdot e^{6\cdot y - y^2\cdot 7} = \frac{\text{d}}{\text{d}y} e^{y\cdot 6 - y^2\cdot 7}
|
3,260 |
c \cdot c^2 - f \cdot f \cdot f = \left(-f + c\right) (f^2 + c \cdot c + fc)
|
-29,026 |
y^8 = y^5 \cdot y^3
|
28,268 |
\frac{1}{\sqrt{2}} = \sin\left(3*π/4\right)
|
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